A comprehensive program of CP studies in heavy flavour decays has to go beyond observing large CP asymmetries in nonleptonic B decays and finding that the sum of the three angles of the KM triangle is consistent with 180. There are many more correlations between observables encoded in the KM matrix; those can be expressed through five KM triangles in addition to the one usually considered. To test the completeness of the KM description one has to obtain a highly overconstrained data set sensitive to O(λ) effects with λ = sin θC . Those fall into two categories: (i) Certain large angles agree to leading order only, yet differ in order λ in a characteristic way. (ii) Two observables angles are – for reasons specific to the KM ansatz – O(λ) and O(λ) thus generating an asymmetry of a few percent and of about 0.1 %, respectively. The former can be measured in Bs → ψη, ψφ without hadronic uncertainty, the latter in Cabibbo suppressed D decays. The intervention of New Physics could boost these effects by an order of magnitude. A special case is provided by D → KS,Lπ + vs. D → KS,Lπ . Finally, CP asymmetries involving D − D̄ oscillations could reach observable levels only due to New Physics.